The energy of a gas per litre is 600 text{ J} | vedclass

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Question

(A) For an ideal gas, the internal energy $U$ is related to pressure $P$ and volume $V$ by the formula: $U = \frac{3}{2} PV$.Given, energy per unit vo

Vedclass · Accepted Answer

$4 	imes 10^5 	ext{ N/m}^2$

Vedclass · Answer

(A) For an ideal gas, the internal energy $U$ is related to pressure $P$ and volume $V$ by the formula: $U = \frac{3}{2} PV$.Given, energy per unit volume (energy density) is $u = \frac{U}{V} = 600 	ext{ J/L}$.Since $1 	ext{ L} = 10^{-3} 	ext{ m}^3$, the energy density in $SI$ units is $u = \frac{600 	ext{ J}}{10^{-3} 	ext{ m}^3} = 6 	imes 10^5 	ext{ J/m}^3$.Using the relation $u = \frac{3}{2} P$, we get $P = \frac{2}{3} u$.Substituting the value of $u$: $P = \frac{2}{3} 	imes 6 	imes 10^5 	ext{ N/m}^2 = 4 	imes 10^5 	ext{ N/m}^2$.

The energy of a gas per litre is $600 \text{ J}$. What will be its pressure?

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